Ferguson and Lowi (2001) propose “bipolar voting” as a solution to the electoral ills of the nation. But their idea of allowing voters to vote either for a candidate (+1 vote) or against a candidate (−1 vote) is not new; it was previously analyzed under the rubric of “negative voting” in Brams (1978) and Brams and Fishburn (1983).

In three-candidate races, negative voting is equivalent to approval voting:

• voting for a candidate is the same as approving of just one;
• voting against a candidate is the same as approving of the other two.

However, if there are four or more candidates, negative voting gives the voter less opportunity to express her preferences. For example, if she thinks that two candidates are acceptable and two are not, at best she can vote for one of the two acceptable candidates, or she can vote against one of the two unacceptable candidates. Under approval voting, by contrast, this voter can express herself “perfectly” by approving of the two acceptable candidates. Thus, approval voting is more flexible than negative voting for expressing preferences.

“Disapproval voting” would allow the voter in the aforementioned example to vote against the two unacceptable candidates. While approving of one set of candidates is logically equivalent to disapproving of the complementary set, psychologically it is probably a different experience. I favor approval voting, because I believe the negativity of present-day campaigns should not be reinforced by a balloting method that asks voters to vote against candidates.